The plane, a Russian-built Tupolev 154, caught fire after slipping off the side of the runway when a tyre burst on landing at the city of Masshad, site of Iran's holiest shrine, state media said.
Pilgrims flock to Mashhad throughout the year to visit the tomb of Imam Reza, the eighth Muslim Shi'ite imam. It was not clear if any of those on board the Iranairtour flight were making the pilgrimage.
State television said 62 people had survived the crash with no injuries, 47 were hospitalised and 30 bodies had been recovered so far.
Nourollah Rezai-Niaraki, head of Iran's civil aviation organisation, told state TV that 43 people on board the plane had been injured but the rest escaped unharmed.
Earlier reports had suggested a death toll of 80.
Television pictures showed a broken-up plane with parts of its fuselage charred. The cockpit appeared to be largely unaffected by the fire, as did much of the rear portion of the aircraft.
Firefighters were shown extinguishing fires in parts of the smouldering wreck and clambering over other areas of the fuselage, carrying out corpses covered in blankets.
The southern city of Bandar Abbas, where the plane began its journey, is the Islamic Republic's main port and is located near the popular Iranian holiday destination of Qeshm island.
An Iranairtour official, who asked not to be identified, said the airline was contacting families of the victims. He also said flights to Mashhad had been cancelled after the crash.
Air safety experts say Iran has a poor safety record, with a string of crashes in recent decades, many involving Russian-made aircraft.
US sanctions on the Islamic state have prevented it from buying new aircraft or spares from the West, forcing it to supplement its ageing fleet of Boeing and Airbus planes with aircraft from the former Soviet Union.